The output of amp 1 is present on the secondary side of the output transformers at amp 2. Depending on the configuration, it could be stepping the signal down and getting into the circuitry of amp 2.
I think you meant to say stepping the signal voltage up. Not down.
I also would think the secondary winding of the output transformers, (of the amp that is turned off), would add a parallel impedance load to the output transformers of the amp being used to drive the speakers. (Speaker coils + secondary windings of output transformers of the off amp.)
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